A modified perturbation method for convective straight fins with temperature-dependent thermal conductivity - Sumio KATO; Shoichi MATSUDA (Mechanical Engineering Journal)
A modified perturbation method (MPM) is applied to obtain the solution of the heat transfer equation for convective fins with temperature-dependent thermal conductivity. In this method, the nonlinear term is split into linear and nonlinear terms to obtain the perturbation solution. The solution of a convective fin with linearly temperature-dependent thermal conductivity by the MPM is simple to use and very accurate. Calculated results show that the solution by the MPM agrees well with the FDM (Finite Difference Method) solution in a wide range of the small parameter ε (thermal conductivity parameter), whereas the solution by the conventional perturbation method (CPM) is accurate only in a small range of ε. For example, the RMS error δRMS of the MPM solution with respect to the FDM solution is less than 10-4 for N (fin parameter) = 1 and -0.505 ≤ ε ≤ 10, on the other hand the RMS error of the CPM solution is less than 10-4 for N = 1 and -0.141 ≤ ε ≤ 0.142. The fin efficiencies obtained by the CPM, MPM and FDM are examined. The modification of the perturbation method by splitting the nonlinear term helps reduce the contribution of the nonlinear term upon the solution, which drastically improves the convergence characteristics of the solution.